On the spectrum of closed k=2 flux tubes in D=2+1 SU(N) gauge theories

TL;DR

This study investigates the energy spectrum of k=2 flux tubes in 2+1 dimensional SU(N) gauge theories, finding they closely follow Nambu-Goto string predictions with notable corrections, and providing insights into effective string interactions.

Contribution

It provides the first detailed analysis of the spectrum of closed k=2 flux tubes in SU(N) gauge theories, highlighting their near Nambu-Goto behavior and interaction patterns.

Findings

Eigenstates mostly belong to SU(N) irreducible representations.

Low-lying states are close to Nambu-Goto string predictions for moderate lengths.

Corrections to string behavior are typically of order one, indicating effective string dynamics.

Abstract

We calculate the energy spectrum of a k=2 flux tube that is closed around a spatial torus, as a function of its length l. We do so for SU(4) and SU(5) gauge theories in 2 space dimensions. We find that to a very good approximation the eigenstates belong to the irreducible representations of the SU(N) group rather than just to its center, Z_N. We obtain convincing evidence that the low-lying states are, for l not too small, very close to those of the Nambu-Goto free string theory (in flat space-time). The correction terms appear to be typically of O(1) in appropriate units, much as one would expect if the bosonic string model were an effective string theory for the dynamics of these flux tubes. This is in marked contrast to the case of fundamental flux tubes where such corrections have been found to be unnaturally small. Moreover we find that these corrections appear to be particularly small when the `phonons' along the string have the same momentum, and large when their momentum is opposite. This provides information about the detailed nature of the interactions in the effective string theory. We have searched for, but not found, extra states that would arise from the excitation of the massive modes presumably associated with the non-trivial structure of the flux tube.